Problem: Solve for $x$ and $y$ using elimination. ${-4x-3y = -20}$ ${-5x+3y = 2}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-9x = -18$ $\dfrac{-9x}{{-9}} = \dfrac{-18}{{-9}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-4x-3y = -20}\thinspace$ to find $y$ ${-4}{(2)}{ - 3y = -20}$ $-8-3y = -20$ $-8{+8} - 3y = -20{+8}$ $-3y = -12$ $\dfrac{-3y}{{-3}} = \dfrac{-12}{{-3}}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-5x+3y = 2}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ + 3y = 2}$ ${y = 4}$